Linked Questions

2
votes
1answer
896 views

Lagrangian formalism and dissipative systems [duplicate]

Why the central concepts of classical mechanics, viz. Lagrangian and Hamiltonian formalisms cannot address constraint forces like friction and others in dissipative systems?
1
vote
0answers
135 views

Which class of Dynamical Systems is governed by Lagrangian Dynamics? [duplicate]

Lagrangian formalism is a technique using which we can obtain the time evolution of a dynamical system. Given a dynamical system, can we say whether or not we can write down a Lagrangian (solving it ...
0
votes
0answers
40 views

Can a Lagrangian be defined for arbitrary physical systems? [duplicate]

For physical systems with conservative forces, we can define a potential function $V$, and a Lagrangian $L=T-V$. At first, I thought that lagrangian mechanics only applied to systems with conservative ...
25
votes
6answers
24k views

What are holonomic and non-holonomic constraints?

I was reading Herbert Goldstein's Classical Mechanics. Its first chapter explains holonomic and non-holonomic constraints, but I still don’t understand the underlying concept. Can anyone explain it to ...
20
votes
3answers
3k views

How do I show that there exists variational/action principle for a given classical system?

We see variational principles coming into play in different places such as Classical Mechanics (Hamilton's principle which gives rise to the Euler-Lagrange equations), Optics (in the form of Fermat's ...
19
votes
2answers
5k views

Lagrangian and Hamiltonian EOM with dissipative force

I am trying to write the Lagrangian and Hamiltonian for the forced Harmonic oscillator before quantizing it to get to the quantum picture. For EOM $$m\ddot{q}+\beta\dot{q}+kq=f(t),$$ I write the ...
15
votes
2answers
4k views

What causes a force field to be “non-conservative?”

A conservative force field is one in which all that matters is that a particle goes from point A to point B. The time (or otherwise) path involved makes no difference. Most force fields in physics ...
7
votes
1answer
8k views

Euler-Lagrange equations with non-conservative force (example)

I am trying to understand how to use the Euler-Lagrange formulation when my system is subject to external forces. Consider the system pictured below: Let's define the lagrangian, as always, as $L =...
3
votes
1answer
3k views

Problems that Lagranges equations of the 1st kind can solve whereas the 2nd kind can't?

Can anyone give examples of mechanics problems which can be solved by Lagrange equations of the first kind, but not the second kind?
5
votes
2answers
2k views

The Equivalency of Newton's Second Law, Hamilton's Principle and Lagrange Equations [closed]

Consider the following question in classical mechanics Are Newton's Second Law, Hamilton's Principle and Lagrange Equations equivalent for particles and system of particles? If Yes, where ...
1
vote
1answer
2k views

Lagrangian Mechanics, When to Use Lagrange Multipliers?

I've seen a few other threads on here inquiring about what is the point of Lagrange Multipliers, or the like. My main question though is, how can I tell by looking at a system in a problem that ...
3
votes
2answers
804 views

Generalized definitions of Lagrangian and Hamiltonian functions

When we enter into the scope of Analytical mechanics we usually start with these two primary notions: Lagrangian function & Hamiltonian function And usually textbooks define Lagrangian as $L=T-V$ ...
3
votes
2answers
1k views

The Role of Friction in The Lagrangian

I'm pretty new to physics (I am presently taking AP Physics 1 though I am far ahead of that in math) and I was reading this paper that found the equations of motion for Atwood's machine using ...
3
votes
4answers
445 views

How do I include friction due to normal force in Lagrange Equations?

I am going through the Goldstein book on classical mechanics and the after he derived the Lagrange equations he used Rayleigh dissipation function to include friction as a generalized force. In school ...
2
votes
1answer
887 views

Non-conservative system and velocity dependent potentials

I'm studying Lagrangian mechanics, but I'm a little bit upset because when dealing with Lagrange's equations, we mostly consider conservative systems. If the system is non conservative they are very ...

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